Graphical Approach to Limits Homework

Q0"5:)7"-'G550/"7:'&/'()3)&*'+'2/3%./01
1)
2)
!!
a) lim! f " x # = -2 b) lim$ f " x # = 2
x 01
d) f "1# = 1
x 01
e) lim f " x # = -2
x 0!1
c) lim f " x # DNE a) lim! f " x # = 3 b) lim$ f " x # = 0
x 01
x 02
x 02
!!
f) lim f " x # ! 2 d) f "2# = 3
e) lim f " x # = 0
x 01
x 0!1
3)
c) lim f " x # DNE
x 02
f) lim f " x # ! !1
x 01
4)
!!
a) lim! f " x # = 1 b) lim$ f " x # = 1
x 03
d) f " 3# = 1
c) lim f " x # ! 1 a) lim! f " x # = 13 b) lim$ f " x # = 13
x 03
x 00
x 00
!!
e) lim f " x # = - ! f) lim f " x # ! 1 d) f "0# = 13
e) lim f " x # = 1
x 03
x 0!1
x 01
x 0!1
5)
c) lim f " x # ! 13
x 00
f) lim f " x # ! 1
x 01
6)
!!
a) lim! f " x # = 0 b) lim$ f " x # = 0
x 0!1
d) f "!1# = DNE
x 0!1
c) lim f " x # ! 0
x 0!1
e) lim f " x # = 1 f) lim f " x # ! 1
x 0!1
x 01
a) lim! f " x # = 1 b) lim$ f " x # = 1
!!!!!
x 01
d) f "1# = 0
x 01
c) lim f " x # ! 1
x 01
e) lim f " x # = -1 f) lim f " x # ! 1
x 0!1
x 01
!!!"#$%&'(#$&)#'*&+(",+-!!."#!$%&'()%*+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!,!9S!,!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!. /&0. /,)!$(&1
7)
8)
!!
a) lim! f " x # = -1 b) lim$ f " x # = 1 c) lim f " x # ! DNE a) lim! f " x # = 1 b) lim$ f " x # = 1
x 01
x 01
x 01
x 03
x 03
!!
d) f "1# = DNE e) lim f " x # = 1 f) lim f " x # ! !2
d) f " 3# = DNE e) lim f " x # = -1
x 0!1
x 01
x 0!1
9)
c) lim f " x # ! 1
x 03
f) lim f " x # ! 0
x 01
10)
!!
a) lim! f " x # = -1 b) lim$ f " x # = -1 c) lim f " x # ! !1
!
x 02
d) f "2# = 1
x 02
e) lim f " x # = 2
x 0!1
x 02
f) lim f " x # ! 2
x 01
a) lim! f " x # = -1 b) lim$ f " x # = -1 c) lim f " x # DNE
!!!
x 00
x 00
d) f "0# = 1
e) lim f " x # = 1
x 0!1
x 00
f) lim f " x # ! 1
x 01
12)
11)
!!
a) lim! f " x # = 0 b) lim$ f " x # = 0 c) lim f " x # ! 0
a) lim! f " x # = 0 b) lim$ f " x # = 0 c) lim f " x # ! 0
d) f "0# = 0
d) f "0# = 0
x 00
x 00
x 00
e) lim f " x #DNE f) lim f " x # DNE
x 0!1
x 01
x 00
x 00
x 00
e) lim f " x # = -1 f) lim f " x # ! 0
x 0!1
x 01
!!!"#$%&'(#$&)#'*&+(",+-!!."#!$%&'()%*+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!,!9T!,!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!. /&0. /,)!$(&1
13)
14)
!!
a) lim! f " x # = -3 b) lim$ f " x # = -2 c) lim f " x # ! DNE
x 01
d) f "1# = -2
x 01
x 01
e) lim f " x # = -3 f) lim f " x # ! 1
x 0!1
a) lim! f " x # = -2 b) lim$ f " x # = -2 c) lim f " x # ! !2
!!!!
x 01
15)
x 01
d) f "1#DNE
x 01
x 01
e) lim f " x # =! f) lim f " x # ! 1
x 0!1
x 01
16)
!!
a) lim! f " x # = -2 b) lim$ f " x # = -2 c) lim f " x # ! !2
x 01
d) f "1# = 0
x 01
e) lim f " x # = 1
x 0!1
x 01
f) lim f " x # ! 1
a) lim! f " x # = 1 b) lim$ f " x # = -1 c) lim f " x # DNE
!!!!!!!
x 01
17)
x 00
d) f "0#DNE
x 00
x 00
e) lim f " x # = 0 f) lim f " x # ! 0
x 0!1
x 01
18)
!!
a) lim! f " x # = 1 b) lim$ f " x # = 1 c) lim f " x # ! 1
x 0!3
d) f "!3#DNE
x 0!3
x 0!3
a) lim! f " x # = 0 b) lim$ f " x # = 0 c) lim f " x # ! 0
!!
x 00
e) lim f " x # = -1 f) lim f " x # ! !2.5 d) f "0# = 0
x 0!1
x 01
x 00
x 00
e) lim f " x #DNE f) lim f " x # ! 0
x 0!1
x 01
!!!"#$%&'(#$&)#'*&+(",+-!!."#!$%&'()%*+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!,!9U!,!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!. /&0. /,)!$(&1